Question

HURRY! Which table represents a linear function?

Answer 1

Remember that to tell if a function is linear for a table, you should look for a constant rate of change, and the only function that has a constant rate of change is the first one.
`x` is increasing by 1, and
`y` is increasing by 0.5.

Now that we know that, lets find the equation of our table.
First, lets take tow points from our table: (1,
`(1)/(2)`) and
`(2,1)`.
Next, use the slope formula:
`m= (y_(2)-y_(1))/(x_(2)-x_(1) )`
We know for our points that
`y_(2)=1`,
`y_(1)= (1)/(2)`,
`x_(2)=2`, and
`x_(1)=1`, so lets replace those point in our formula to find
`m`:

`m= (1- (1)/(2) )/(2-1)`

`m= (1)/(2)`

Finally, we can use the point slope formula
`y-y_(1)=m(x-x_(1))` to find our equation:

`y- (1)/(2) = (1)/(2) (x-1)`

`y- (1)/(2) = (1)/(2) x- (1)/(2)`

`y= (1)/(2)x`

We can conclude that the first table represents a linear function, and its equation is
`y= (1)/(2)x`